Almost entropic matroids

Frantisek Matus
Czech Academy of Sciences (AVCR)

A matroid with the ground set N is almost entropic (aent) if its rank function can be approximated by the Shannon entropies of all the subvectors of a random vector that is indexed by N. More precisely, the rank function must be the limit of such approximations. We will review known results and open problems on the class of aent matroids and compare it with other classes of matroids.
The role of aent matroids in the information theory, secret sharing and network coding will be discussed.

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